It is currently 21 Oct 2017, 13:04

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If n is an integer, is n even?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129150 [1], given: 12194

If n is an integer, is n even? [#permalink]

### Show Tags

26 Aug 2012, 03:12
1
KUDOS
Expert's post
4
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

80% (00:53) correct 20% (00:56) wrong based on 1373 sessions

### HideShow timer Statistics

If n is an integer, is n even?

(1) n^2 - 1 is an odd integer.
(2) 3n + 4 is an even integer.

Practice Questions
Question: 27
Page: 277
Difficulty: 600
[Reveal] Spoiler: OA

_________________

Kudos [?]: 129150 [1], given: 12194

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129150 [4], given: 12194

Re: If n is an integer, is n even? [#permalink]

### Show Tags

26 Aug 2012, 03:13
4
KUDOS
Expert's post
4
This post was
BOOKMARKED
SOLUTION:

If n is an integer, is n even?

(1) n^2 - 1 is an odd integer --> $$n^2-1=odd$$ --> $$n^2=odd+1=even$$. Now, since $$n$$ is an integer, then in order $$n^2$$ to be even $$n$$ must be even. Sufficient.
Notice that if we were not told that $$n$$ is an integer, then $$n$$ could be some irrational number (square root of an even number), for example $$\sqrt{2}$$, so not an even integer.

(2) 3n + 4 is an even integer --> $$3n + 4=even$$ --> $$3n=even-4=even$$. The same here, since $$n$$ is an integer, then in order $$3n$$ to be even $$n$$ must be even. Sufficient.
Notice that if we were not told that $$n$$ is an integer, then $$n$$ could be some fraction, for example $$\frac{2}{3}$$, so not an even integer.

_________________

Kudos [?]: 129150 [4], given: 12194

Intern
Joined: 16 Oct 2011
Posts: 2

Kudos [?]: 1 [0], given: 26

Re: If n is an integer, is n even? [#permalink]

### Show Tags

27 Aug 2012, 09:07
If n is an integer, is n even?

(1) n^2 - 1 is an odd integer.
(2) 3n + 4 is an even integer.

If n^2 - 1 is odd ,then n^2 is even.Assuming both Positive and Negative integers fall under even category,I ca say n is even.

So statement 1 is alone sufficient.

If 3n + 4 is an even integer,then 3n is also even. Since 3 is odd, n has to be even.

So statement 2 is also sufficient.

Kudos [?]: 1 [0], given: 26

Intern
Joined: 28 Aug 2012
Posts: 45

Kudos [?]: 48 [0], given: 3

Location: Austria
GMAT 1: 770 Q51 V42
Re: If n is an integer, is n even? [#permalink]

### Show Tags

30 Aug 2012, 11:32
(1) n^2 - 1 is odd. The next consecutive integer is n^2 and is therefore even. This means that n must be even too, because squaring a number does NOT change this. --> sufficient

(2) 3n + 4 is even. So 3n is even, too. This means that the prime factorization of 3n includes at least one 2. Dividing by 3 (to get from 3n to n) does NOT eliminate recude the number of twos in the prime factorization, so n is even. --> sufficient

The correct answer is D. Both statements are individually sufficient.

Kudos [?]: 48 [0], given: 3

Manager
Status: exam is close ... dont know if i ll hit that number
Joined: 06 Jun 2011
Posts: 189

Kudos [?]: 30 [0], given: 1

Location: India
GMAT Date: 10-09-2012
GPA: 3.2
Re: If n is an integer, is n even? [#permalink]

### Show Tags

30 Aug 2012, 19:56
i will go with d
both options individually can get the required info
-as its an integer no more fractions
integer when squared gives the same type value i.e odd gives odd and even gives even
same way multiplying odd with even gives even and odd with odd gives odd

hence both are individually sufficient
_________________

just one more month for exam...

Kudos [?]: 30 [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129150 [1], given: 12194

Re: If n is an integer, is n even? [#permalink]

### Show Tags

31 Aug 2012, 02:33
1
KUDOS
Expert's post
SOLUTION:

If n is an integer, is n even?

(1) n^2 - 1 is an odd integer --> $$n^2-1=odd$$ --> $$n^2=odd+1=even$$. Now, since $$n$$ is an integer, then in order $$n^2$$ to be even $$n$$ must be even. Sufficient.
Notice that if we were not told that $$n$$ is an integer, then $$n$$ could be some irrational number (square root of an even number), for example $$\sqrt{2}$$, so not an even integer.

(2) 3n + 4 is an even integer --> $$3n + 4=even$$ --> $$3n=even-4=even$$. The same here, since $$n$$ is an integer, then in order $$3n$$ to be even $$n$$ must be even. Sufficient.
Notice that if we were not told that $$n$$ is an integer, then $$n$$ could be some fraction, for example $$\frac{2}{3}$$, so not an even integer.

_________________

Kudos [?]: 129150 [1], given: 12194

Intern
Affiliations: CA, SAP FICO
Joined: 22 Nov 2012
Posts: 33

Kudos [?]: 12 [0], given: 51

Location: India
Concentration: Finance, Sustainability
Schools: Mannheim"18
GMAT 1: 620 Q42 V33
GMAT 2: 720 Q47 V41
GPA: 3.2
WE: Corporate Finance (Energy and Utilities)
Re: If n is an integer, is n even? [#permalink]

### Show Tags

16 Mar 2014, 18:55
Bunuel wrote:
SOLUTION:

If n is an integer, is n even?

(1) n^2 - 1 is an odd integer --> $$n^2-1=odd$$ --> $$n^2=odd+1=even$$. Now, since $$n$$ is an integer, then in order $$n^2$$ to be even $$n$$ must be even. Sufficient.
Notice that if we were not told that $$n$$ is an integer, then $$n$$ could be some irrational number (square root of an even number), for example $$\sqrt{2}$$, so not an even integer.

(2) 3n + 4 is an even integer --> $$3n + 4=even$$ --> $$3n=even-4=even$$. The same here, since $$n$$ is an integer, then in order $$3n$$ to be even $$n$$ must be even. Sufficient.
Notice that if we were not told that $$n$$ is an integer, then $$n$$ could be some fraction, for example $$\frac{2}{3}$$, so not an even integer.

Since n is a integer, can we not try with n as 0?

Kudos [?]: 12 [0], given: 51

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129150 [0], given: 12194

Re: If n is an integer, is n even? [#permalink]

### Show Tags

16 Mar 2014, 23:45
X017in wrote:
Bunuel wrote:
SOLUTION:

If n is an integer, is n even?

(1) n^2 - 1 is an odd integer --> $$n^2-1=odd$$ --> $$n^2=odd+1=even$$. Now, since $$n$$ is an integer, then in order $$n^2$$ to be even $$n$$ must be even. Sufficient.
Notice that if we were not told that $$n$$ is an integer, then $$n$$ could be some irrational number (square root of an even number), for example $$\sqrt{2}$$, so not an even integer.

(2) 3n + 4 is an even integer --> $$3n + 4=even$$ --> $$3n=even-4=even$$. The same here, since $$n$$ is an integer, then in order $$3n$$ to be even $$n$$ must be even. Sufficient.
Notice that if we were not told that $$n$$ is an integer, then $$n$$ could be some fraction, for example $$\frac{2}{3}$$, so not an even integer.

Since n is a integer, can we not try with n as 0?

Yes, n can be 0 but 0 is even too.
_________________

Kudos [?]: 129150 [0], given: 12194

Manager
Joined: 04 Oct 2013
Posts: 162

Kudos [?]: 119 [0], given: 55

Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: If n is an integer, is n even? [#permalink]

### Show Tags

18 Mar 2014, 06:45
If n is an integer, is n even?

(1) $$n^2 - 1$$ is an odd integer.
(2) $$3n + 4$$is an even integer.

Given that, n is an integer.

Statement (1)

$$n^2 - 1=(n-1)(n+1)$$ is odd =>$$(n-1)$$ and $$(n+1)$$ both are odd => $$n$$ is even......Sufficient ....A B C D E

Statement (2)

$$3n + 4$$ is even =>$$3n + 3$$ is odd => $$3(n+1)$$ is odd =>$$n + 1$$ is odd =>$$n$$ is even ........Sufficient....A B C D E

Since, each statement alone is sufficient, answer is (D).

Kudos [?]: 119 [0], given: 55

Senior Manager
Joined: 20 Aug 2015
Posts: 396

Kudos [?]: 336 [0], given: 10

Location: India
GMAT 1: 760 Q50 V44
Re: If n is an integer, is n even? [#permalink]

### Show Tags

09 Dec 2015, 00:06
Bunuel wrote:
If n is an integer, is n even?

(1) n^2 - 1 is an odd integer.
(2) 3n + 4 is an even integer.

Given: n is an integer
Required: is n even?

Statement 1: $$n^2$$ - 1 is an odd integer
$$n^2$$ - 1 = (n-1)(n+1) = odd.
This means both n-1 and n+1 are odd
Odd*Odd = Odd
Odd*Even = Even
Even*Even = Even

n-1, n, n+1 are three consecutive integers.
Since we know that both n-1 and n+1 are odd
Hence n has to be even.

SUFFICIENT

Statement 2: 3n + 4 is an even integer
Even + Even = Even
Even + Odd = Odd
Odd + Odd + Odd

Since 3n+4 = even and 4 is an even integer.
Hence 3n = even. Therefore n = even
SUFFICIENT

Option D
_________________

Reach out to us at bondwithus@gmatify.com

Kudos [?]: 336 [0], given: 10

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1648

Kudos [?]: 847 [0], given: 3

Location: United States (CA)
Re: If n is an integer, is n even? [#permalink]

### Show Tags

09 Aug 2016, 13:33
Expert's post
1
This post was
BOOKMARKED
Quote:
If n is an integer, is n even?

(1) n^2 - 1 is an odd integer.
(2) 3n + 4 is an even integer.

We need to determine whether integer n is even. Let's review four facts about even and odd integers: 1) An integer and its square are either both even or both odd. 2) The sum (or difference) between an even integer and an odd integer is always odd. 3) The sum of two even integers (or two odd integers) is always even. 4) If the product of two integers is even, at least one of them must be even.

Statement One Alone:

(n^2) - 1 is an odd integer.

Since (n^2) - 1 is an odd integer, we know that n^2 must be even and thus n must be even. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

3n + 4 is an even integer.

Since 3n + even = even integer, we know that 3n must be even, and since 3 is odd, n must be even. Statement two is sufficient to answer the question.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 847 [0], given: 3

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2212

Kudos [?]: 844 [0], given: 595

If n is an integer, is n even? [#permalink]

### Show Tags

22 Aug 2016, 02:18
We need to find if x is even or odd
given => x is an integer
statement 1 =>n^2-1=odd => n^2=> even => n must be even
Rule used => POWER Does not effect the even / odd nature of any number

statement 2 => 3n+4=even=> 3n=even => n must even
Rulw => if XY=even => at-least one of them must be even
Hence suff

Smash that D
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 844 [0], given: 595

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2212

Kudos [?]: 844 [0], given: 595

Re: If n is an integer, is n even? [#permalink]

### Show Tags

03 Dec 2016, 18:23
Here is my solution ->
Her we need to get the Even/Odd nature of integer n
Lets dive into statements
Statement 1
n^2-1=odd
so n^2 must be even
RULE-> POWER Does not affect the even/odd nature of any integer
Hence n must be even too.
Hence Sufficient
Statement 2->
3n+4=even
Hence 3n=even-even=even
As 3n=even and 3 is odd => n must be even to make 3n even
Hence Sufficient
Hence D

_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 844 [0], given: 595

Director
Joined: 02 Sep 2016
Posts: 776

Kudos [?]: 41 [0], given: 267

Re: If n is an integer, is n even? [#permalink]

### Show Tags

01 Apr 2017, 10:19
Bunuel wrote:
If n is an integer, is n even?

(1) n^2 - 1 is an odd integer.
(2) 3n + 4 is an even integer.

Practice Questions
Question: 27
Page: 277
Difficulty: 600

(1) The even odd nature of n=n^2 (e.g. 2=Even and 2^2=4=Even)
Therefore just writing n-1= Odd
Even- Odd=Odd
1 is odd. Therefore n is even.

(2) 3n+4=Even
Only two possible cases:
Even+Even= Even
Odd+Odd=Even

4 is even and the even or odd nature of 3n depends on n.
Thus n is even. (Therefore 3n=Even)

Sufficient.

D

Kudos [?]: 41 [0], given: 267

Re: If n is an integer, is n even?   [#permalink] 01 Apr 2017, 10:19
Display posts from previous: Sort by